To test the safety of two doses of a drug, hydroxyurea, given alone or together with another drug, DDI, in persons infected with the HIV. This study also will see if hydroxyurea given alone or together with DDI decreases the amount of virus in the blood of HIV-infected persons as compared to DDI given alone. In addition, how DDI and hydroxyurea are absorbed into the body will also be looked at. Hydroxyurea has been used in a large number of sickle cell patients, but its use in HIV-infected persons is new and has been limited.